Properties of Equality

The following are the
properties of equality
for real numbers
. Some textbooks list just a few of them,
others list them all. These are the logical rules which allow you to
balance, manipulate, and solve equations.

PROPERTIES
OF EQUALITY

Reflexive Property

For all real numbers
x
,
x
=
x
.

A number equals itself.

These
three properties define an
equivalence relation

Symmetric Property

For all real numbers
x
and
y
,

if
x
=
y
, then
y
=
x
.

Order of equality does not matter.

Transitive Property

For all real numbers
x
,
y
,
and
z
,

if
x
=
y
and
y
=
z
, then
x
=
z
.

Two numbers equal to the same number are equal to each other.

Addition Property

For all real numbers
x
,
y
,
and
z
,

if
x
=
y
, then
x
+
z
=
y
+
z
.

These properties
allow you to balance and solve equations involving real numbers